Ten years ago I let the battery in the Honda3000 run down and did not replace it. I just use the pull cord ever since. But I would have had to use a trickle charger to keep that battery up between using the gen since the gen does not get enough run time or used often enough to keep the battery up.
The gen rides in the back of the truck so a couple years ago I got the idea of using the truck battery to start the gen so I wouldn't have to use the pull cord. I did run wires from the gen's inside battery compartment to hang outside the gen and I keep the ends of those wires covered when not in use (wire nuts)
I made an adapter to go from the slide-in camper plug the truck has (behind the cab and in front of the box) over to the wires I added to the gen. So with that plugged in, the electric start worked.
Since that worked, I don't see why if there were a proper battery in the gen, that you couldn't attach a trickle charger to those added wires hanging out and keep the gen's battery charged.
BTW I gave up on my electric start method even though it worked as it was too much bother with the adapter, and am back to using the pull cord, but the wires that I added are still hanging out of the gen.
1. 1991 Oakland 28DB Class C
on Ford E350-460-7.5 Gas EFI
Photo in Profile
2. 1991 Bighorn 9.5ft Truck Camper on 2003 Chev 2500HD 6.0 Gas
See Profile for Electronic set-ups for 1. and 2.